Module 11: Innovation & Patents Market Organization & Public Policy (Ec 731) George Georgiadis · Technological progress is crucial for improving welfare, but (very) costly. ◦ – How to incentivize firms to innovate? Suppose that a large number of firms engage in Cournot competition. ◦ – We have seen that the equilibrium price will be close to the marginal cost, and firms’ profits close to 0. – Consider a firm’s incentive to engage in costly R&D. – If other firms can imitate a new innovation, then the innovating firm will have little incentive to invest in the first place. – Therefore, a new firm must be guaranteed enough (expect) profits to recoup the R&D cost. Enter: Patents (that provide the innovating firm with a temporary monopoly). ◦ Schumpeter (1943): If one wants to induce firms to undertake R&D, then one must ◦ accept the creation of monopolies as a necessary evil. The Value of Innovation A simple model of process innovation: ◦ – Assume that innovation lowers the (constant) marginal production cost fromc ¯ to c < c¯. – How much would a firm be willing to pay to reduce its marginal cost, given that no other firm will (be allowed to) buy it? 1 Social Planner (First best): She sets price equal to marginal cost; i.e., p =¯c before the innovation, and p = c after. ◦ s u¯ Additional net social surplus p.u of time: v = u D(c)dc ◦ ´ The social planner’s value from innovating is: ◦ c¯ s 1 rt s 1 V = e− v dt = D(c)dc ˆ0 r ˆc Monopoly: Suppose that a firm is in a monopoly situation. ◦ Let ⇧m denote monopoly profit p.u of time. Then: ◦ d⇧ d m = [(p c) D(p)] dc dc − @⇧ dpm @⇧ = m + m = D (pm(c)) @p dc @c − =0 – Application of the Envelope| Theorem{z } . The monopolist’s value from innovating is: ◦ m 1 rt m m V = e− [⇧ (c) ⇧ (¯c)] dt ˆ0 − 1 c¯ d⇧m = dc r ˆ − dc c ✓ ◆ 1 c¯ = D (pm(c)) dc r ˆc m m m s Because p (c) >cand D0 < 0, we have D (p (c)) <D(c) for all c, and hence V <V . ◦ A monopolist has weaker incentives to innovate relative to a social planner. ◦ – Intuitively: Because he sets a higher price, the cost reduction pertains to a smaller number of units. Competition: Suppose that 2 firms engage in Bertrand competition. ◦ 2 – Then p =¯c, and firms earn 0 profits. The firm that obtains new technology with cost c is awarded a patent. ◦ Let pm(c) be the monopoly price when the cost is c. ◦ Case 1: If pm(c) c¯, then we say that the innovation is drastic. ◦ – The innovator then charges p = pm(c), and obtains the entire market. – His value from innovating is V m. Case 2: If pm(c) > c¯, then we say that the innovation is nondrastic. ◦ – Both firms charge p =¯c, and the innovator’s profit p.u of time is ⇧c =(¯c c) D (¯c). − – The value from innovating is 1 V c = (¯c c) D (¯c) r − – Becausec<p ¯ m(c) <pm(c), we have D(¯c) >D(pm(c)) for all c c,so ≥ 1 c¯ 1 c¯ V m = D (pm(c)) dc < D (¯c) dc = V c r ˆc r ˆc s 1 c¯ 1 c¯ c – But D (¯c) <D(c) for all c<c¯,soV = r c D(c)dc > r c D(¯c)dc = V . ´ ´ – Therefore, V c (V s,Vm). 2 Take-aways: ◦ – Even with patents of infinite duration, the innovator does not internalize the entire social surplus from the innovation. – A monopolist has less to gain from innovating than does a competitive firm. Why? Monopoly Threatened By Entry Simple setting with two firms. Initially: ◦ – Firm 1 is a monopolist, produces at marginal costc ¯, and earns profit ⇧m (¯c). – Firm 2 does not currently produce, but is a potential entrant. 3 If only one of the firms has the opportunity to acquire the technology to reduce marginal ◦ cost to c, then we have the same situation as before: – V c >Vm, so innovation is more valuable for the entrant than for the monopolist. Now suppose that a 3rd party generates the innovation, and auctions it to the two firms. ◦ We will see that in this case, the innovation is more valuable for the monopolist than ◦ for the entrant. If firm 1 obtains the innovation, then it remains a monopolist, and earns profit ⇧m (c). ◦ If firm 2 obtains the innovation, then both firms become duopolists. ◦ – Denote the profits of firm 1 and 2 by ⇧d (¯c, c) and ⇧d (c, c¯), respectively. The value of innovation for firm 1 is: ◦ ⇧m (c) ⇧d (¯c, c) V m = − r The value of innovation for firm 2 is: ◦ ⇧d (c, c¯) V c = r Assume that: ⇧m (c) ⇧d (c, c¯)+⇧d (¯c, c). ◦ ≥ – A monopolist earns greater profit than two non-colluding duopolists. Then: V m >Vc. (Opposite from before!) ◦ Because competition reduces profits, the monopolist’s incentive to remain a monopolist ◦ is greater than the entrant’s incentive to become a duopolist. A monopolist may have incentives to obtain property rights on an innovation, even ◦ though he will make no use of it (often referred to as patent shelving). – The only purpose is to prevent an entrant from competing. 4 – Subject of many antitrust cases; generally considered anti-competitive behavior. – In many countries, the patent law includes a compulsory licensing provision (i.e., patent holder is forced to license if he does not utilize the innovation within a specified length of time). Patent Races Insofar, we have considered ◦ 1. the value of innovation in a situation where one firm has monopoly over R&D activities; and 2. the value of innovation when monopoly power is auctioned to a monopolist and a potential entrant. In practice, R&D competition can be likened to a “race” for a patent. ◦ – Multiple firms invest in R&D simultaneously, and whichever firm innovates first, obtains a patent. We will study the so-called “Poisson” patent race. ◦ – Initially, there is a monopolist with costc ¯, and a potential entrant. – The two firms compete in R&D activities, and the firm first to innovate (i.e., obtain a technology with cost c) obtains a patent. At every moment t, each firm i invests in R&D at rate x , and its innovation rate is ◦ i,t h(xi,t)dt, where h0 > 0 >h00. – If firm i invests xi during (t, t + dt), then it incurs cost xidt and its probability of innovating is h(xi,t)dt. – This is called a“Poisson”race, because the probability of innovating during (t, t + dt) is independent of investments at t0 <t. – It follows that each firm’s investment rate will be independent of t. If firm 1 obtains the patent, then the firms earn profits ⇧m (c) and 0, respectively. ◦ 5 If firm 2 obtains the patent, then the firms earn profits ⇧d (¯c, c) and ⇧d (c, c¯), respec- ◦ tively. Assume that: ⇧m (c) ⇧d (c, c¯)+⇧d (¯c, c). ◦ ≥ During an arbitrary interval (t, t + dt), firms 1 and 2 earn profit [⇧m(¯c) x ] dt and ◦ − 1 x dt, respectively. − 2 – With probability h(x1)dt, firm 1 is first to innovate, and the firms will earn dis- m ⇧ (c) x1 − counted profits r and 0, respectively. – With probability h(x2)dt, firm 2 is first to innovate, and the firms will earn dis- ⇧d(¯c,c) ⇧d(c,c¯) counted profits r and r , respectively. – With probability 1 h(x )dt h(x )dt, neither firm innovates during (t, t + dt). − 1 − 2 The value of innovation to firm 1 is ◦ m d m rdt ⇧ (c) ⇧ (¯c, c) V =[⇧(¯c) x ] dt + e− h(x )dt + h(x )dt +(1 h(x )dt h(x )dt) V 1 − 1 1 r 2 r − 1 − 2 1 m ⇧m(c) ⇧d(¯c,c) ⇧ (¯c) x1 + h(x1) + h(x2) = − r r r + h(x1)+h(x2) and for firm 2 d rdt ⇧ (c, c¯) V = x dt + e− h(x ) +(1 h(x )dt h(x )dt) V 2 − 2 2 r − 1 − 2 2 ⇧d(c,c¯) x2 + h(x2) = − r r + h(x1)+h(x2) rdt – Note 1: e− 1 rdt for “small” dt (Taylor expansion) ' − – Note 2: dt2 0 ' A Nash equilibrium is a pair x1⇤,x2⇤ such that xi⇤ maximizes Vi given x⇤ i. ◦ { } − Which firm will have stronger incentives to invest in R&D? ◦ Depends on which of two e↵ects dominates. ◦ 1. Efficiency e↵ect:⇧m (c) ⇧d (c, c¯)+⇧d (¯c, c) suggests that the monopolist has ≥ stronger incentives, and therefore, spends more on R&D. 6 2. Replacement e↵ect: By increasing x1, the monopolist (on expectation) brings the discovery date forward, thus hastening his own replacement. In contrast, the entrant does not forgo a flow profit during the R&D phase, and therefore has stronger incentives. What if we consider the case of a drastic innovation? ◦ – i.e., whichever firm obtains the patent, becomes a monopolist, so ⇧d (c, c¯)=⇧m (c) and ⇧d (¯c, c)=0. Problems: ◦ – Excessive duplication of research – With multiple stages, as the gap between the firm widens, incentives weaken. Welfare Analysis of Patent Protection Overall, economic research in this area is still nascent. ◦ Main issues: ◦ – Optimal patent length? – Optimal degree of patent protection? – Subsidies? (e.g., in the US, tax credits for R&D investments) An example from United States vs. Microsoft Corp: ◦ – Microsoft was accused of becoming a monopoly and engaging in abusive practices, in violation of the Sherman Act.